Imagine, Tom is in a room with only one girl. The two are talking to each
other and you ask somebody whether he knows this girl. Here the relative clause
is non-defining because in this situation it is obvious which girl you mean.

Do you know the girl, who is talking to Tom?

Note: In non-defining relative clauses, who/which may not be
replaced with that.

Object pronouns in non-defining relative clauses must be used.

Jim, who/whom we met yesterday, is very nice.

When the relative pronoun refers back to a person and is
the subject of the non-defining relative clause, who is used, e.g.:

The woman, who later died in hospital, has
not yet been named.

When the relative pronoun refers back to a thing and is the
subject of the non-defining relative clause, which is used, e.g.:

This new project, which begins in September, will
cost several million pounds.

When the relative pronoun refers back to a person and is
the object of the non-defining relative clause, who or whom are used, e.g.:

Her previous manager, who she had never liked, retired
six months ago.

Edwards brother, whom she later married, never
spoke to his parents again.

Register note.
As in defining relative clauses, whom is rather formal and would
only be used in written English or formal spoken English.

When the relative pronoun refers back to a thing and is the
object of the non-defining relative clause, which is used, e.g.:

This bar of chocolate, which he devoured immediately,
was the first thing he had eaten in two days.

Note that, unlike in defining relative clauses, there is no
zero relative pronoun,
i.e. the pronoun cannot be left out when it is
functioning as the object of the relative clause, cf:

He was a distant cousin who/whom/that she had never met.
(defining)

He was a distant cousin she had never met.
(defining)

A distant cousin, who/whom she had never met, was
meeting her for lunch. (non-defining)